CN112885471B - Psoriasis curative effect evaluation system based on Bayesian network maximum entropy self-learning extension set pair analysis - Google Patents
Psoriasis curative effect evaluation system based on Bayesian network maximum entropy self-learning extension set pair analysis Download PDFInfo
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Abstract
The invention relates to a psoriasis curative effect evaluation system based on Bayesian network maximum entropy self-learning extension set pair analysis, which comprises the following steps: selecting diseases for efficacy evaluation, and constructing a efficacy evaluation Bayesian network; inviting experts to grade, and obtaining each index weight by using an AHP method; the AHP weight is used as an initial weight to be combined with a Bayesian network for self-learning, the information entropy is set to reach the maximum value, and the weight after self-learning is output; obtaining the comprehensive weight of the symptom index according to the hierarchical relation of the Bayesian network; constructing a curative effect evaluation ESPA model based on the obtained symptom index comprehensive weight, and calculating CD corresponding to each patient symptom index; the patient's efficacy is evaluated. Its advantages are: a disease comprehensive evaluation network of a plurality of clinical indexes is constructed through Bayesian network analysis, and is combined with the maximum entropy principle, the index weight is determined through the self-learning process, and on the basis, the disease curative effect is evaluated by utilizing an extended set to assist clinical decision.
Description
Technical Field
The invention relates to the technical field of curative effect evaluation, in particular to a psoriasis curative effect evaluation system based on Bayesian network maximum entropy self-learning extended set pair analysis.
Background
The evaluation of curative effect is always the key point of clinical diagnosis and treatment and clinical research. Various Psoriasis evaluation tools have been proposed to evaluate the Severity of Psoriasis, the most common of which are Psoriasis Area and Severity Index (PASI) and Body Surface Area (BSA), however Psoriasis is a systemic disease, the way of efficacy evaluation from skin lesions is not comprehensive enough and is greatly influenced by physician subjectivity, and the World Health Organization (WHO) also points out that PASI and clinical outcome indicators such as the skin disease Quality of Life Index (DLQI) currently in use need improvement. The low correlation between the degree of reduction in the quality of life of psoriasis patients and the severity of skin lesions has also been found in some studies, indicating that the quality of life of psoriasis patients is an important aspect in the assessment of efficacy. The pathology of psoriasis relates to a natural immune system and an acquired immune system, and immunological indexes in serum of a patient are different from those of normal people, so that reference can be provided for evaluating the curative effect.
At present, some mathematical models have been used for evaluating the efficacy of a disease. For example, brugnara G, utilizes an Artificial Neural Network (ANN) to automatically and quantitatively evaluate Multiple Sclerosis (MS) disease burden on Magnetic Resonance Imaging (MRI), and finds that ANN is more accurate in evaluating MS patient disease burden. Xu W and the like apply binary Logistic regression analysis to analyze and compare the correlation between the 14 indexes and the coronary heart disease, and the result shows that when the binary Logistic regression analysis is applied to evaluate the relationship between the risk factors and the coronary heart disease, the reliability and the effectiveness of the analysis can be improved by strictly controlling the confounding factors. However, the above efficacy evaluation model has no fixed model or needs to evaluate diseases by controlling confounding factors, and fails to construct a relatively stable evaluation system by combining various clinical data.
Because the disease evaluation is influenced by multiple layers and factors, constructing a reasonable disease evaluation comprehensive network with multiple symptom indexes and determining the relative importance degree of the disease evaluation comprehensive network is the basis of scientific disease evaluation. A bayesian network is a probabilistic model based on Directed Acyclic Graph (DAG), and is an important method for expressing uncertainty knowledge and performing prediction. The method can find causal relations among variables from data and reveal the strength of the causal relations through probability. Therefore, the action relationship of different indexes on the curative effect can be described through the Bayesian network, and a corresponding comprehensive relationship network is constructed.
The importance degree of the symptom index on the curative effect evaluation is objectively and accurately determined, which is a premise for effective disease evaluation. Therefore, the weight of the symptom index plays an important role in the efficacy evaluation. The current weight determination method comprises subjective weight and objective weight. The main subjective weighting methods, such as Analytic Hierarchy Process (AHP), best Worst Method (BWM), and the like, determine the weighting values by expert experience and according to the target importance, and are greatly influenced by human factors. The main objective weighting methods include entropy weighting and weighting with a certain specific expression of the target, which vary with the variation of the evaluation object. Therefore, the organic combination of subjective methods based on clinical experience and objective methods based on the detailed performance of the indicators is the key to determining the weights of the symptom indicators reasonably and effectively. Entropy is a parameter describing the disorder of an objective object, can reflect the uncertainty of a random variable, and when the entropy is maximum, means that the added constraints and assumptions are minimum, and the true state of the object is most likely to be approached, namely, the maximum entropy principle is met. Therefore, the disease comprehensive evaluation network constructed based on a plurality of clinical indexes combines the AHP subjective weight method and the maximum entropy principle, so that the entropy of the whole network is maximized, the corresponding weight is minimally influenced by subjective consciousness, and the weight result is more objective.
Set Pair Analysis (SPA) is a mathematical method for studying deterministic and uncertain interconnections and interactions, searching for implicit valuable information and revealing the potential regularity of the information, and is proposed in 1989 by the scholar of the world, zhao Chong Ji. The method is applied to many aspects such as system decision, comprehensive evaluation, prediction and the like. The traditional SPA model needs to set the symptom grade of the patient and a corresponding threshold value when calculating the Connection Degree (CD) of the evaluation index. In consideration of the clinical situation that the symptom index cannot be subjected to importance level grading or the importance level corresponding to the symptom index and the corresponding threshold are not clear, the traditional set-pair analysis method needs to be improved so that the curative effect evaluation can be still carried out under the situation that the symptom index level or the threshold is not determined.
In summary, 1, the existing curative effect evaluation method can only evaluate the disease according to a single symptom index by controlling confounding factors, and cannot construct a systematic evaluation system by integrating clinical data in multiple aspects; 2. the existing weight calculation method cannot give consideration to subjective and objective combination, and cannot reflect the weight through actual data; 3. the traditional CD calculation of the SPA model has the limitations of grade and threshold.
Chinese patent documents: CN202010508271.3, application No. 2020.06.06, with the patent names: a drug curative effect multi-index evaluation method based on a Bayesian network and a three-dimensional mathematical model. The method comprises the steps of firstly, acquiring original experiment data of an evaluation drug according to a preset template, preprocessing the original experiment data, and obtaining final experiment data for evaluation; then carrying out heterogeneity analysis on the final experimental data, and respectively processing the final experimental data based on the heterogeneity size to obtain a Meta analysis evidence relation graph; then, calculating the relative ranking of the drug effects based on a multidimensional Bayes model, and obtaining an area value under a cumulative ranking probability graph according to the relative ranking; and finally, carrying out multidimensional clustering on the drug effects of the drugs based on the area values under the cumulative sorting probability map to finish the classification of the drug effects of the drugs.
Chinese patent documents: CN201911012531.1, application date 2019.10.23, patent names: and (4) researching recurrence factors and prevention and treatment of psoriasis based on set pair analysis partial association coefficients. Discloses a method for researching recurrence factor of psoriasis and prevention and cure thereof based on set pair analysis partial union coefficient, comprising materials and method, result and conclusion; the material and method comprises data source and research method; the result is composed of identification of psoriasis recurrence high-risk factors based on uncertain theory, identification of psoriasis recurrence high-risk factors based on a joint coefficient potential function, and calculation of partial joint coefficients of psoriasis Chinese and western medical therapy recurrence trend.
In the method for evaluating the curative effect of a drug based on a bayesian network and a three-dimensional mathematical model in the patent document CN202010508271.3, the method includes firstly, collecting original experimental data of the evaluated drug according to a preset template, and preprocessing the original experimental data to obtain final experimental data for evaluation; then, heterogeneity analysis is carried out on final experimental data, and the scheme of the invention fills up the blank in drug efficacy evaluation based on a Bayesian method and cluster analysis under multi-junction indexes, so that the evaluation and classification results of drug efficacy are more accurate and have more referential performance; in patent document CN201911012531.1, the advantages of studying the recurrence factor and prevention and treatment of psoriasis based on set pair analysis partial association coefficient are shown as follows: the RCT research proves that the optimized set pair analysis diagnosis and treatment scheme improves the clinical curative effect, and proves the feasibility and the scientificity of the set pair analysis in the traditional Chinese medicine clinical practice and the diagnosis and treatment research to a certain extent; the invention is based on published psoriasis literature data, and the analysis bias connection coefficient is secondarily analyzed by an application set, so that the psoriasis recurrence risk factor and prognosis trend are analyzed, and a new scientific basis is provided for the prevention and treatment of psoriasis.
The invention relates to a method and a system for evaluating clinical curative effect based on Bayesian network maximum entropy self-learning and extended set pair analysis, which evaluate clinical curative effect by combining clinical performance, laboratory indexes, quality of life and accompanying symptoms, constructs a disease comprehensive evaluation network of a plurality of clinical indexes through Bayesian network analysis, combines with a maximum entropy principle, determines index weight through a self-learning process, evaluates disease curative effect by utilizing an extended set pair analysis on the basis of the index weight, and provides support for auxiliary clinical decision.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, and provides a disease curative effect evaluation method and system based on Bayesian network maximum entropy self-learning and extended set pair analysis, which evaluate clinical curative effects of multiple aspects such as comprehensive clinical performances, laboratory indexes, quality of life and accompanying symptoms, construct a disease comprehensive evaluation network of multiple clinical indexes through Bayesian network analysis, combine with a maximum entropy principle, determine index weights through a self-learning process, evaluate the disease curative effects by utilizing an extended set on the basis of the index weights, and provide support for auxiliary clinical decision.
In order to realize the purpose, the invention adopts the technical scheme that:
a psoriasis curative effect evaluation system based on Bayesian network maximum entropy self-learning extended set pair analysis, the system comprises the following steps:
s1, selecting diseases for evaluating curative effect, selecting disease curative effect related symptom indexes, and constructing a Bayesian network for evaluating curative effect according to mutual relation among the disease curative effect related symptom indexes;
s2, inviting experts to respectively grade symptom indexes of each layer of the curative effect evaluation Bayesian network according to importance to obtain expert grades; on the basis, acquiring each index weight by using an AHP method and carrying out consistency check;
s3, performing self-learning by taking the AHP weight as an initial weight and combining a Bayesian network, setting the information entropy to reach a maximum value, and outputting the weight after the self-learning;
s4, obtaining the comprehensive weight of the symptom index according to the hierarchical relation of the Bayesian network;
s5, constructing a curative effect evaluation ESPA model based on the obtained comprehensive weight of the symptom indexes, and calculating CDs corresponding to the symptom indexes of the patients; after obtaining the CD, calculating the corresponding core contact degree, diversity degree and similarity degree, and finally obtaining the Euclidean distance between the CD and an ideal patient to evaluate the curative effect of the patient.
A psoriasis curative effect evaluation method based on Bayesian network maximum entropy self-learning extension set pair analysis comprises the following steps:
a bayesian network with N nodes can be represented by N = ((X, T), P)), where (X, T) represents DAG and X is the set of all nodes in DAG, i.e., X = { X) = 1 ，x 2 ，…，x n }; t is a set of directed edges among the nodes and represents the incidence relation among the node variables; p is a Conditional Probability Table (CPT) at each node, CPT representing the logical relationship between nodes; when the Bayesian network has a plurality of nodes X = { X = { X } 1 ，x 2 ，…，x n When it is, according to the chain rule, the joint probability distribution is:
wherein P is ai Is node x i A set of parent nodes;
the maximum entropy calculation formula of the weight can be obtained according to the maximum entropy criterion:
where ω is the weight value of the attribute, ω ij ∈N i ，N i Is a set of weights under the same target at the same level in the bayesian network; in the self-learning process, the maximum entropy is used as an output condition;
in the evaluation of the curative effect, a Bayesian network is trained by using a gradient descent method; let S be S training samples X 1 ，X 2 ，…，X s ω is an attribute initial weight value of a parent variable CPT, which is calculated by AHP according to the following steps; according to the influence of the criterion layer on the target layer, inviting experts to grade according to the importance pairs to obtain a comparison matrix marked as A; according to the influence of the analysis layers on the criterion layer, constructing a comparison matrix of each analysis layer, and recording the comparison matrix as B1, B2, ·, bn; carrying out normalization processing on the comparison matrix to obtain a relative weight vector; calculating a maximum characteristic root based on the relative weight vector, and carrying out consistency check; if the consistency test is not passed, the expert reclassifies and then calculates to determine the initial weight;
in a Bayesian network for efficacy evaluation, ω for each layer should satisfy Σ ω i ＝1；p(e|X d ) Indicating e node at sample X d The lower prior probability value is equivalent to the attribute value in the CPT; the gradient descent strategy adopts a greedy hill climbing method; these weights are modified in each iteration and eventually converge to a locally optimal solution, i.e. the total probability value:
according to ln P W (S) calculating a gradient, for each attribute and evaluation index in each network structure, the gradient being:
going forward a small step in the gradient direction, the update weight is:
wherein l is the learning rate of the step length and is a small constant;
since ω ∈ [0, 1]]And omega of the same layer attribute satisfies sigma omega i =1, normalizing the weight after iteration by normalizing again;
setting the end condition of weight self-learning to be that the information entropy reaches the maximum value, carrying out entropy calculation on the weight obtained after iteration, and carrying out iteration solving again by taking the obtained weight value as the initial weight when the weight value is not the maximum value; stopping computing iteration and finishing when the maximum value is reached, wherein the output result is the self-learning weight based on the combination of Bayes and the maximum entropy and the subjective and objective combination; finally, obtaining the comprehensive weight of the symptom index according to the hierarchical relation of the Bayesian network;
in a system, two sets A and B with a certain relationship form a set pair H (A, B), and the set is assumed to have N characteristics, wherein S is the number of characteristics shared in the set pair, P is the number of characteristics opposite in the set pair, F is the number of uncertain characteristics in the set pair, and S + P + F = N; the obtainable contact degree is:
where a = S/N represents identity, b = F/N represents disparity, c = P/N represents oppositivity, and a + b + c =1, then where i is the coefficient of disparity, ie ∈ [ -1,1], j is the coefficient of oppositivity, typically specified as-1;
if the symptom weight is considered, the total association is:
for symptom index k, if a larger value of the data indicates a better clinical effect, a smaller value of the data indicates a poor treatment effect; for the data of symptom index k in patient l, let the maximum and minimum values of the data be the upper threshold u, respectively k And a lower threshold v k (ii) a Suppose for arbitrary x kl ∈[u k ,v k ]Then equation (9) or equation (10) may be defined to calculate x kl And u k The proximity of (a);
x is due to kl And u k And v k Is 1, so equation (11) or equation (12) may be defined to calculate x kl And v k The proximity of (c) is:
let the product of the formulas (9) and (10) be x kl And u k The proximity of (c):
let the product of the equations (11) and (12) be x kl And v k The proximity of (c):
two proximities are combined and expressed as a function:
from this, the first and second derivatives of this function are:
when x is kl ＝u k Or x kl ＝v k Equation (15) takes the maximum value, which in this case is:
let x kl And u k Are the same degree, while letting x kl And v k Proximity of (A) is the degree of opposition, defined by a, b, c ∈ [0, 1] mentioned above](ii) a Therefore, the maximum value obtained by equation (18) is set as the normalized quotient, x kl And u k Of (a) and x kl And v k Is in [0, 1]]Within the range of (a), carrying out normalization treatment to obtain:
if a + b + c =1 is satisfied, then
Finally, patient/has a relationship to symptom k of:
conversely, if a larger value of the symptom index k represents poor curative effect, a smaller value represents better clinical efficacy; accordingly, patient/has a relationship to symptom k of:
after obtaining the contact degree of each patient, the curative effect of each patient can be ranked by comparing the values of the contact degrees; for a determined degree of connectivity μ, CDC is introduced to analyze the characteristics of a set pair H = (a, B), and then by it identity and opponency are compared; the core contact degree is an important indication reflecting the characteristics of the SPA, and can be calculated by the defined formula (24):
C(μ)＝a-c (24)
wherein C (μ) represents the core relatedness of μ;
to rank the efficacy of each patient, the contact degrees of each patient need to be compared; therefore, DD was introduced to describe the diversity of multiple patients; suppose that x and y of any two patients with efficacy assessment are linked by μ x ＝a x +b x i+c x j，μ y ＝a y +b y i+c y j, calculating the diversity degree, the identity degree, the difference degree and the opposition degree of the core association degrees of the two patients according to the formula (25) to the formula (28):
D CDC (μ x ，μ y )＝|C(μ x )-C(μ y )| (25)
D a (μ x ，μ y )＝|a x -a y | (26)
D b (μ x ，μ y )＝|b x -b y | (27)
D c (μ x ，μ y )＝|c x -c y | (28)
wherein D CDC (u x ,u y )，D a (u x ,u y )，D b (u x ,u y ) And D c (u x ,u y ) Respectively represent two patients mu x And mu y The diversity degree, identity, difference and contrast of the corresponding core contact degrees;
thereafter, SD was introduced to reflect the similarity of multiple patients; equation (29) for calculating μ for two patients x And mu y SD corresponding to degree of relation, and it follows that the range of SD is [0, 1%](ii) a When the value of SD is close to 1, it means that patient x and patient y are more similar; then the SD for the two patient contacts is:
wherein S (u) x ,u y ) Represents any two patients mu x And mu y SD corresponding to degree of relation, SD is in the range of [0,1 ∈]；
The SD is then further processed using the ideal patient; the ideal patient set by us is the best curative effect and is used for comparing patients for clinical curative effect evaluation; according to the definition of SPA, CD of ideal patient with optimal curative effect is defined as formula (30);
μ safety ＝1+0·i+0·j (30)
wherein mu safety Indicating the degree of association of the ideal patient for optimal efficacy.
Using ED to assess patient-to-patient and ideal patient-to-ideal correlations; ED is used as a straight line distance measurement and can be used for evaluating the relevance of fuzzy linguistic variables; the SD of each patient in the study was thus assessed using ED to confirm the correlation of the assessment with the best-performing patient; however, since a plurality of symptom indices are considered in the efficacy evaluation using the extended set pair analysis, and the weight of each symptom index is generally different; if the symptom index weights are taken into account in the calculation of ED, the ED of the evaluated patient and the ideal patient is:
wherein d (. Mu.) l ，u * ) ED, μ representing the degree of association between patient/and ideal patient kl Represents the contact of patient l for symptom k; if the ED is smaller, the curative effect of the patient is better; if the ED is larger, the curative effect of the patient is worse.
The invention has the advantages that:
1. comprehensively evaluating the curative effect by considering the influence of multiple factors: because clinical curative effect evaluation relates to various factors such as individual difference, environmental factors and the like, some methods for evaluating the curative effect, such as Logistic regression analysis, can only distinguish two classification variables, and a Bayesian network can find the relation between various symptom indexes and the curative effect and quantitatively express the strength of the relation; therefore, the Bayesian network analysis can describe the relationship and strength between various symptom indexes and the curative effect, and the model is more practical based on clinical practical data.
2. Combining the host and the guest to obtain the weight: in the traditional AHP, a judgment matrix needs to be repeatedly and manually modified in the weight calculation process, and different experts have large differences in evaluation of index weights, so that evaluation results are greatly influenced by subjective factors; therefore, according to the maximum entropy criterion, the optimal weight value is actively output through a self-learning method on the basis of the known subjective weight, and the accuracy is higher.
3. Quantitative description of efficacy evaluation results: the obtained results of some curative effect evaluation methods are often not intuitive enough, for example, a certain mathematical statistics basis is needed for explaining the curative effect evaluation results of Logistic regression analysis, the early-stage constructed cloud-to-cloud curative effect evaluation model represents the curative effect grade of a patient through a cloud picture but cannot intuitively reflect the curative effect result of the patient in the same grade, and the curative effect evaluation through the ESPA model can not only quantitatively describe the clinical curative effect of the patient through ED, but can clearly reflect the difference of the curative effect for the curative effect of different patients.
4. Overcomes the defects of the traditional SPA: traditional SPA models rely on class classification data, and CD calculation of evaluation indices requires classification of patient symptom classes and their corresponding thresholds for efficacy assessment. ESPA is improved in an SPA method, CD is converted into ED with specific numerical values for evaluating the curative effect, the curative effect evaluation can be still carried out under the condition that the symptom grade or the threshold value is unknown, and the application range of the curative effect evaluation is improved.
Drawings
FIG. 1 is a schematic diagram of a Bayesian network for evaluating the efficacy of psoriasis vulgaris in accordance with the present invention.
FIG. 2 is a weight comparison diagram of AHP and Bayesian maximum entropy self-learning of the present invention.
FIG. 3 is a schematic diagram of the stability analysis result of Bayesian maximum entropy self-learning of the present invention.
FIG. 4 is a graph showing the results of sensitivity analysis of efficacy evaluation of 20 patients according to the present invention.
Detailed Description
The invention is further described with reference to the following examples and with reference to the accompanying drawings.
Example 1
The invention relates to a psoriasis curative effect evaluation method and a psoriasis curative effect evaluation system based on Bayesian network maximum entropy self-learning extended set pair analysis, wherein the psoriasis curative effect evaluation system comprises the following steps:
s1, selecting diseases for evaluating curative effects, selecting disease curative effect related symptom indexes, and constructing a Bayesian network for evaluating curative effects according to mutual relation among the disease curative effect related symptom indexes;
s2, inviting experts to respectively grade symptom indexes of each layer of the curative effect evaluation Bayesian network according to importance to obtain expert grades; on the basis, acquiring each index weight by using an AHP method and carrying out consistency check;
s3, performing self-learning by taking the AHP weight as an initial weight and combining a Bayesian network, setting the information entropy to reach a maximum value, and outputting the weight after the self-learning;
s4, obtaining the comprehensive weight of the symptom index according to the hierarchical relation of the Bayesian network;
s5, constructing a curative effect evaluation ESPA model based on the obtained symptom index comprehensive weight, and calculating CD corresponding to each patient symptom index; after obtaining the CD, the corresponding Core Degree (CDC), diversity Degree (DD), and Similarity Degree (SD) are calculated, and finally, the Euclidean Distance (ED) from the ideal patient is obtained to evaluate the curative effect of the patient.
The specific method comprises the following steps:
a bayesian network with N nodes can be represented by N = ((X, T), P)), where (X, T) represents DAG and X is the set of all nodes in DAG, i.e., X = { X) = 1 ，x 2 ，…，x n }; t is a set of directed edges among the nodes and represents the incidence relation among the node variables; p is a Conditional Probability Table (CPT) on each node, CPT representing the logical relationship between nodes; when the Bayesian network has a plurality of nodes X = { X = { X } 1 ，x 2 ，…，x n When it is, according to the chain rule, the joint probability distribution is:
wherein P is ai Is node x i A set of parent nodes;
the maximum entropy calculation formula of the weight can be obtained according to the maximum entropy criterion:
where ω is the weight value of the attribute, ω ij ∈N i ，N i Is a set of weights under the same target at the same level in the bayesian network; in the self-learning process, the maximum entropy is used as an output condition;
in the evaluation of the curative effect, a Bayesian network is trained by using a gradient descent method; let S be S training samples X 1 ，X 2 ，…，X s ω is an attribute initial weight value of a parent variable CPT, which is calculated by AHP according to the following steps; according to the influence of the criterion layer on the target layer, inviting experts to grade according to the importance pairs to obtain a comparison matrix which is marked as A; according to the influence of the analysis layers on the criterion layer, constructing a comparison matrix of each analysis layer, and recording the comparison matrix as B1, B2, ·, bn; normalizing the comparison matrix to obtain a relative weight vector; calculating a maximum characteristic root based on the relative weight vector, and carrying out consistency check; if the consistency test is not passed, the expert reclassifies and then calculates to determine the initial weight;
in a Bayesian network for efficacy evaluation, ω for each layer should satisfy Σ ω i ＝1；p(e|X d ) Indicating e node at sample X d The prior probability value of the following, namely the attribute value in the CPT is equivalent; the gradient descent strategy adopts a greedy hill climbing method; these weights are modified in each iteration and eventually converge to a locally optimal solution, i.e. the total probability value:
according to ln P W (S) calculating a gradient, for each attribute and evaluation index in each network structure, the gradient being:
proceeding a small step in the gradient direction, the update weight is:
wherein l is the learning rate of the step length and is a small constant;
since ω ∈ [0, 1]]And omega of the same layer attribute satisfies sigma omega i =1, normalizing the weight after iteration by normalizing again;
setting the end condition of weight self-learning to be that the information entropy reaches the maximum value, carrying out entropy calculation on the weight obtained after iteration, and carrying out iteration solution again by taking the obtained weight value as the initial weight when the weight value is not the maximum value; stopping computing iteration and finishing when the maximum value is reached, wherein the output result is the self-learning weight based on the combination of Bayes and the maximum entropy and the subjective and objective combination; finally, obtaining the comprehensive weight of the symptom index according to the hierarchical relation of the Bayesian network;
in a system, two sets A and B with a certain relation form a set pair H (A, B), and the set is assumed to have N characteristics, wherein S is the number of characteristics shared by the set pair, P is the number of characteristics opposite to the set pair, F is the number of uncertain characteristics in the set pair, and S + P + F = N; the available contact degree is:
where a = S/N represents identity, b = F/N represents disparity, c = P/N represents opposition, and a + b + c =1, then where i is the coefficient of disparity, i e ∈ [ -1,1], j is the coefficient of opposition, typically specified as-1;
if the symptom weight is considered, the total association is:
for symptom index k, if a larger value of the data indicates a better clinical effect, a smaller value of the data indicates a poor treatment effect; for data of symptom index k in patient l, let the maximum sum of dataMinimum values are respectively the upper threshold values u k And a lower threshold v k (ii) a Suppose for arbitrary x kl ∈[u k ,v k ]Then equation (9) or equation (10) may be defined to calculate x kl And u k The proximity of (a);
x is due to kl And u k And v k Is 1, so equation (11) or equation (12) may be defined to calculate x kl And v k The proximity of (c) is:
let the product of the formulas (9) and (10) be x kl And u k The proximity of (c):
let the product of the equations (11) and (12) be x kl And v k The proximity of (c):
two proximities are combined and expressed as a function:
it follows that the first and second derivatives of this function are:
when x is kl ＝u k Or x kl ＝v k When the maximum value is obtained by equation (15), the maximum value in this case is:
let x kl And u k Are the same degree, while letting x kl And v k Proximity of (A) is the degree of opposition, defined by a, b, c ∈ [0, 1] mentioned above](ii) a Therefore, the maximum value obtained by equation (18) is set as the normalized quotient, x kl And u k Of (a) and x kl And v k In the proximity of [0, 1]]Within the range of (a), carrying out normalization treatment to obtain:
if a + b + c =1 is satisfied, then
Finally, patient/has a relationship to symptom k of:
conversely, if a larger value of the symptom index k represents poor curative effect, a smaller value represents better clinical efficacy; accordingly, patient/has a relationship to symptom k of:
after obtaining the contact degree of each patient, the curative effect of each patient can be ranked by comparing the values of the contact degrees; for a determined degree of connectivity μ, CDC is introduced to analyze the characteristics of a set pair H = (a, B), and then by it identity and opponency are compared; the core contact degree is an important indication reflecting the characteristics of the SPA, and can be calculated by the defined formula (24):
C(μ)＝a-c (24)
wherein C (μ) represents the core relatedness of μ;
to rank the efficacy of each patient, the contact degrees of each patient need to be compared; therefore, DD was introduced to describe the diversity of multiple patients; let us assume that x and y of any two patients with efficacy assessment are associated with mu x ＝a x +b x i+c x j，μ y ＝a y +b y i+c y And i, calculating the diversity degree, the identity degree, the difference degree and the opposition degree of the core contact degrees of the two patients according to the formula (25) to the formula (28) respectively:
D CDC (μ x ，μ y )＝|C(μ x )-C(μ y )| (25)
D a (μ x ，μ y )＝|a x -a y | (26)
D b (μ x ，μ y )＝|b x -b y | (27)
D c (μ x ，μ y )＝|c x -c y | (28)
wherein D CDC (u x ,u y )，D a (u x ,u y )，D b (u x ,u y ) And D c (u x ,u y ) Respectively represent two patients mu x And mu y The diversity degree, identity, difference and contrast of the corresponding core contact degrees;
thereafter, SD was introduced to reflect the similarity of multiple patients; equation (29) for calculating μ for two patients x And mu y SD corresponding to degree of relation, and it follows that the range of SD is [0, 1%](ii) a When the value of SD is close to 1, it means that patient x and patient y are more similar; then the SD for the two patient contacts is:
wherein S (u) x ,u y ) Represents any two patients mu x And mu y SD corresponding to degree of relation, SD is in the range of [0,1 ∈]；
The SD is then further processed using the ideal patient; the ideal patient set by us is the best curative effect and is used for comparing patients for clinical curative effect evaluation; according to the definition of SPA, CD of ideal patient with optimal curative effect is defined as formula (30);
μ safety ＝1+0·i+0·j (30)
wherein mu safety Indicating the degree of association of the ideal patient for optimal efficacy.
Using ED to assess patient-to-patient and ideal patient-to-ideal correlations; ED is used as a straight line distance measurement and can be used for evaluating the relevance of fuzzy linguistic variables; thus, the SD of each patient in the study was assessed using ED to confirm the correlation of the assessment with the best-performing patient; however, since a plurality of symptom indices are considered in the efficacy evaluation using the extended set pair analysis, and the weight of each symptom index is generally different; if the symptom index weights are taken into account in the calculation of ED, the ED of the evaluated patient and the ideal patient is:
wherein d (μ) l ，u * ) ED, μ, representing the degree of connection between patient/and ideal patient kl Represents the contact of patient l for symptom k; if the ED is smaller, the curative effect of the patient is better; if the ED is larger, the curative effect of the patient is worse.
The invention is further illustrated by the following evaluation of the efficacy of psoriasis vulgaris as an example:
1. clinical data
All cases were confirmed to be psoriasis vulgaris patients from the dermatology clinic of Yueyang Chinese and western medicine combination hospital affiliated to Shanghai medical university. The research divides psoriasis vulgaris patients into three subgroups of blood heat syndrome group (BHS), blood stasis syndrome group (BSS) and non-blood heat non-blood stasis syndrome group (NHS). Participants will be grouped according to the traditional Chinese medicine syndrome classifications and receive oral traditional Chinese medicine herbal treatments (classified according to traditional Chinese medicine syndrome and tailored to the participants' disease progression). Study duration was 16 weeks, including 8 weeks of intervention treatment, 8 weeks of follow-up. The test was registered with Clinical Trials. Gov (ID: NCTNCT 03942185) and approved by the ethical Committee of the Yueyang Chinese and Western medicine combination Hospital, university of medicine, shanghai (appendix proceedings 2019-030). Research and observation show 100 patients with psoriasis vulgaris in the dermatology clinic and ward of the Yueyang Chinese and western medicine combination hospital affiliated to Shanghai medicine university in 10 months in 2019 to 4 months in 2020. The group with blood heat syndrome had 39 men and 9 women; the age is 21-63 years, and the average (42.60 +/-10.00) years. The patients with blood stasis syndrome are 23 men and 10 women; age 29-65 years, mean (44.70 + -10.01) years. 11 male cases and 8 female cases of the patients with non-blood heat and non-blood stasis syndrome; age 31-65 years, mean (49.68 ± 9.01) years. The comparison difference of each group of general data has no statistical significance (P is more than 0.05).
2. Index for evaluating therapeutic effect
The patients were evaluated by selecting the psoriasis vulgaris associated with skin lesions area PASI and BSA, immunological related indexes SCC, TNF-alpha, IL-10, IL-17, IL-22, IL-23, C3, C4, quality of life related DLQI, ZUNG Self-Rating Anxiety Scale (SAS) and ZUNG Self-Rating Depression Scale (SDS), and oral dryness Questionnaire (Xerostomia Questionaire, XQ) accompanied by symptoms of dry mouth, constipation and Sleep, constipation Rating Scale (CCS), pittsburgh Sleep Quality Index Scale (PSQI) as the criteria for efficacy evaluation. The patient's symptom indices were evaluated at the end of the 8 week intervention treatment and blood samples were taken from the patients. The concentration of IL-10, IL-17, IL-22, IL-23, SCC, TNF-alpha, C3 and C4 in peripheral blood of a patient is measured, venous blood of the patient with psoriasis is collected, 3ml is centrifuged at 2000r/min for 5min, 500 mu L of serum is taken, and the serum is stored at-40 ℃ for detection. Values are taken by an enzyme-linked immunosorbent assay (Finland Leibbo model: MK 3), a standard curve is drawn by ELISA software, and the concentration is calculated by an IMS cell image analysis system. The procedures were performed according to kit instructions, and the ELISA kit was purchased from RayBiotech, USA.
3. Constructing a Bayesian network maximum entropy self-learning model and calculating weight
A Bayesian network for efficacy evaluation was constructed from psoriasis vulgaris-associated symptom indicators (see FIG. 1), the first layer including Skin damage (Skin loss Condition), laboratory Index (Laboratory Index), quality of Life (Life Quality) and concomitant Symptoms (Accompaning Symptoms), the second layer including PASI, BSA, SCC, TNF-a, complement (Complement), interleukin (Interleukin), QIDLDLR, ZUNG Self-Rating Anxiety Scale (Self-Rating Anxiety Scale, SAS) and ZUNG Self-Rating Depression Scale (SDS), as well as the Xerostomia Questionaire (XQ), constipation Score (CCS), pittsburgh Sleep Quality Index Scale (PSQI), and IL-10, IL-17, IL-22, IL-23, C3, C4 on the third level. The research invites 10 dermatologists to score the symptom indexes of each layer of the Bayesian network according to importance respectively to obtain expert scores (see Table 1).
Table 1.10 experts' importance scoring results for psoriasis vulgaris associated symptom indexes
On the basis, the AHP is used to obtain each index weight, and the weight result passes the consistency test (see Table 2).
Weight and consistency test result of Table 2.AHP calculation
It is reasonable to state that AHP weights based on expert scores. And then, self-learning is carried out by taking the AHP weight as an initial weight and combining the AHP weight with a Bayesian network, and when the information entropy reaches the maximum value, the self-learned weight is obtained (see fig. 2). And finally, obtaining the comprehensive weight of the symptom index according to the hierarchical relation of the Bayesian network (see Table 3).
Table 3.AHP calculation weight is compared with comprehensive weight obtained by Bayes maximum entropy self-learning model
And carrying out stability analysis on the model to detect the relation among the sample size, the self-learning times and the entropy value. The results of the model stability analysis (see fig. 3) show that the entropy value gradually stabilizes as the sample size increases and the number of self-learning times increases. When the sample size of the research is reached, namely n =100, the entropy value is basically stable, which shows that the research is relatively stable when a Bayesian maximum entropy self-learning model is constructed based on actual data of 100 patients, and weight calculation can be performed by using the model.
4. Constructing an ESPA curative effect evaluation model to analyze the curative effect of a patient
The maximum entropy self-learning weight of the Bayesian network is found to be stable and reliable through stability analysis, so that the ESPA is continuously utilized to evaluate the curative effect of 100 patients on the basis of the weight. The ED is ranked from small to large, with smaller ED corresponding to better treatment (Table 4).
Table 4. Effect ranking results of partial patients ED
The results show that the first five patients with better curative effect are L1 (0.3196), L18 (0.3713), L17 (0.3722), L37 (0.3906) and L21 (0.4126), and the five patients with poorer curative effect are L100 (0.7904), L90 (0.7749), L61 (0.7656), L82 (0.7469) and L99 (0.7400). The difference between the ED of the best curative effect and the ED of the worst curative effect reaches 0.4708, which shows that the curative effect of the same patient is still greatly different when the same patient is treated by the same traditional Chinese medicine method.
The result of the efficacy assessment will be affected by considering the uncertainty of the input in the actual process. Therefore, sensitivity analysis was performed on the final calculation results to check the consistency of the obtained therapeutic effect results. The results of the sensitivity analysis of 20 patients randomly selected (see fig. 4) showed that the ED of the remaining patients varied only slightly or not significantly with the patient data set as variable inputs, indicating that the ESPA efficacy evaluation model was relatively stable.
The invention has the advantages that:
1. the treatment effect is comprehensively evaluated by considering the influence of multiple factors: because clinical curative effect evaluation relates to various factors such as individual difference, environmental factors and the like, some methods for evaluating the curative effect, such as Logistic regression analysis, can only distinguish two classification variables, and a Bayesian network can find the relation between various symptom indexes and the curative effect and quantitatively express the strength of the relation; therefore, the Bayesian network analysis can describe the relationship and strength between various symptom indexes and the curative effect, and the model is more practical based on clinical practical data.
2. The host and the guest combine to obtain the weight: in the traditional AHP, repeated artificial modification needs to be carried out on the judgment matrix in the weight calculation process, and different experts have large differences in evaluation on the index weight, so that the evaluation result is greatly influenced by subjective factors; therefore, according to the maximum entropy criterion, on the basis of the known subjective weight, the optimal weight value is actively output through a self-learning method, and the accuracy is higher.
3. Quantitative description of efficacy evaluation results: the obtained results of some curative effect evaluation methods are often not intuitive enough, for example, a certain mathematical statistics basis is needed for explaining the curative effect evaluation results of Logistic regression analysis, the early-stage constructed cloud-to-cloud curative effect evaluation model represents the curative effect grade of a patient through a cloud picture but cannot intuitively reflect the curative effect result of the patient in the same grade, and the curative effect evaluation through the ESPA model can not only quantitatively describe the clinical curative effect of the patient through ED, but can clearly reflect the difference of the curative effect for the curative effect of different patients.
4. Overcomes the defects of the traditional SPA: traditional SPA models rely on class classification data, and CD calculation of evaluation indices requires classification of patient symptom classes and their corresponding thresholds for efficacy assessment. ESPA is improved in an SPA method, CD is converted into ED with specific numerical values for evaluating the curative effect, the curative effect evaluation can be still carried out under the condition that the symptom grade or the threshold value is unknown, and the application range of the curative effect evaluation is improved.
The foregoing is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, various modifications and additions can be made without departing from the principle of the present invention, and these should also be considered as the protection scope of the present invention.
Claims (1)
1. A psoriasis curative effect evaluation system based on Bayesian network maximum entropy self-learning extended set pair analysis is characterized by comprising the following steps:
s1, selecting diseases for evaluating curative effects, selecting disease curative effect related symptom indexes, and constructing a Bayesian network for evaluating curative effects according to mutual relation among the disease curative effect related symptom indexes;
a bayesian network with N nodes can be represented by N = ((X, T), P), where (X, T) represents a DAG, the DAG is a directed acyclic graph, X is a set of all nodes in the DAG, i.e., X = { X = 1 ，x 2 ，…，x n }; t is a set of directed edges between nodes and represents the association relation between node variables; p is a conditional probability table CPT on each node, and CPT represents the logical relationship between nodes; when the Bayesian network has a plurality of nodes X = { X = { X } 1 ，x 2 ，…，x n In time, according to the chain rule, the joint probability distribution is:
wherein P is ai Is node x i A set of parent nodes;
the maximum entropy calculation formula of the weight can be obtained according to the maximum entropy criterion:
wherein m represents m symptom indexes
N i Is a set of weights under the same target at the same level in the bayesian network; in the self-learning process, the maximum entropy is used as an output condition;
s2, inviting experts to respectively grade symptom indexes of each layer of the curative effect evaluation Bayesian network according to importance to obtain expert grades; on the basis, acquiring each index weight by using an AHP method and carrying out consistency check;
in the evaluation of the curative effect, a Bayesian network is trained by using a gradient descent method; let S be S training samples X 1 ，X 2 ，…，X s ω is an attribute initial weight value of a parent variable CPT, which is calculated by AHP according to the following steps; according to the influence of the criterion layer on the target layer, inviting experts to grade according to the importance to obtain a comparison matrix which is marked as A; according to the influence of the analysis layers on the criterion layer, constructing a comparison matrix of each analysis layer, and recording the comparison matrix as B1, B2, ·, bn; carrying out normalization processing on the comparison matrix to obtain a relative weight vector; calculating a maximum characteristic root based on the relative weight vector, and carrying out consistency check; if the consistency test is not passed, re-scoring by an expert and then calculating to determine the initial weight;
in a Bayesian network for efficacy evaluation, ω for each layer should satisfy Σ ω i ＝1；p(e|X d ) Indicating e node at sample X d The prior probability value of the following, namely the attribute value in the CPT is equivalent; the gradient descent strategy adopts a greedy hill climbing method; these weights are modified in each iteration and eventually converge to a local optimal solution, i.e. the sum of probabilities:
according to ln P W (S) calculating a gradient, for each attribute and evaluation index in each network structure, the gradient being:
going forward a small step in the gradient direction, the update weight is:
wherein l is the learning rate of the step length;
since omega belongs to [0, 1]]And omega of the same layer attribute satisfies sigma omega i =1, normalizing the weight after iteration by normalizing again;
setting the end condition of weight self-learning to be that the information entropy reaches the maximum value, carrying out entropy calculation on the weight obtained after iteration, and carrying out iteration solution again by taking the obtained weight value as the initial weight when the weight value is not the maximum value; stopping computing iteration and finishing when the maximum value is reached, wherein the output result is an objective self-learning weight based on the combination of Bayes and the maximum entropy; finally, obtaining the comprehensive weight of the symptom index according to the hierarchical relation of the Bayesian network;
s3, self-learning is carried out by taking the AHP weight as an initial weight and combining a Bayesian network, the information entropy is set to reach the maximum value, and the weight after self-learning is output;
in a system, two sets A and B with a certain relationship form a set pair H (A, B), and the set is assumed to have N characteristics, wherein S is the number of characteristics shared in the set pair, P is the number of characteristics opposite in the set pair, F is the number of uncertain characteristics in the set pair, and S + P + F = N; the available contact degree is:
where a = S/N represents identity, b = F/N represents disparity, c = P/N represents opposition, and a + b + c =1, then where i is the coefficient of disparity, i e ∈ [ -1,1], j is the coefficient of opposition, typically specified as-1;
if symptom weights are considered, the total degree of association is:
for the symptom index k, if the value of the data is larger, the curative effect is better, and the value is smaller, the curative effect is poor; for the data of symptom index k in patient l, let the maximum and minimum values of the data be the upper threshold u, respectively k And a lower threshold v k (ii) a Suppose for arbitrary x kl ∈[u k ，v k ]Then, the formula (9) and the formula (10) can be defined to calculate x kl And u k The proximity of (a);
x is due to kl And u k And v k Is 1, equations (11) and (12) can be defined to calculate x kl And v k The proximity of (c) is:
let the product of the formulas (9) and (10) be x kl And u k The proximity of (c):
let the product of the equations (11) and (12) be x kl And v k Proximity of (a):
two proximities are combined and expressed as a function:
it follows that the first and second derivatives of this function are:
when x is kl ＝u k Or x kl ＝v k When the maximum value is obtained by equation (15), the maximum value in this case is:
let x kl And u k Are the same degree, while letting x kl And v k Is the degree of opposition, represented by a, b, c ∈ [0, 1] mentioned above](ii) a Therefore, the maximum value obtained by equation (18) is set as the normalized quotient, x kl And u k Of (a) and x kl And v k Is in [0, 1]]Within the range of (a), carrying out normalization treatment to obtain:
if a + b + c =1 is satisfied, then
Finally, patient/has a relationship to symptom k of:
conversely, if a larger value of the symptom index k represents poor curative effect, a smaller value represents better clinical efficacy; accordingly, patient/has a relationship to symptom k of:
after obtaining the contact degree of each patient, the curative effect of each patient can be ranked by comparing the values of the contact degree; for a determined degree of connectivity μ, a core degree of connectivity CDC is introduced to analyze the characteristics of the set pair H = (a, B), and then by means of it the identity and the opponency are compared; the core connectivity, which is an important indicator of the set of responses to the characteristics of the analysis SPA, can be calculated by the defined equation (24):
C(μ)＝a-c (24)
wherein C (μ) represents the core connectivity of μ;
s4, acquiring the comprehensive weight of the symptom index according to the hierarchical relation of the Bayesian network;
to rank the efficacy of each patient, the contact degrees of each patient need to be compared; thus, the degree of diversity DD is introduced to describe the diversity of multiple patients; let us assume that x and y of any two patients with efficacy assessment are associated with mu x ＝a x +b x i+c x j，μ y ＝a y +b y i+c y j, calculating the diversity degree, the identity degree, the difference degree and the opposition degree of the core association degrees of the two patients according to the formula (25) to the formula (28):
D CDC (μ x ，μ y )＝|C(μ x )-C(μ y )| (25)
D a (μ x ，μ y )＝|a x -a y | (26)
D b (μ x ，μ y )＝|b x -b y | (27)
D c (μ x ，μ y )＝|c x -c y | (28)
wherein D CDC (u x ，u y )，D a (u x ，u y )，D b (u x ，u y ) And D c (u x ，u y ) Respectively represent two patients mu x And mu y The diversity degree, identity, difference degree and opposition degree of the corresponding core contact degrees;
thereafter, a degree of similarity SD was introduced to reflect the similarity of multiple patients; equation (29) for calculating μ for two patients x And mu y SD corresponding to degree of relation, and it follows that the range of SD is [0, 1%](ii) a When the value of SD approaches 1, it indicates that patient x and patient y are more similar; then the SD for the two patient contacts is:
wherein S (u) x ，u y ) Represents any two patients mu x And mu y SD corresponding to degree of relation, SD is in the range of [0,1 ∈]；
The SD is then further processed using the ideal patient; the ideal patient set by us is the best curative effect for comparing patients for clinical efficacy evaluation; according to the definition of SPA, the contact degree CD of the optimal curative effect ideal patient is defined as formula (30);
μ safety ＝1+0·i+0·j (30)
wherein mu safety The contact degree of the ideal patient with the optimal curative effect is represented;
s5, constructing a curative effect evaluation extension set pair analysis model based on the obtained symptom index comprehensive weight,
calculating CD corresponding to each patient symptom index; after the CD is obtained, calculating the corresponding core contact degree, diversity degree and similarity degree, and finally obtaining the Euclidean distance between the CD and an ideal patient to evaluate the curative effect of the patient;
using the euclidean distance ED to assess the correlation between patients and ideal patients; ED is used as a straight line distance measurement and can be used for evaluating the relevance of fuzzy linguistic variables; the SD of each patient in the study was thus assessed using ED to confirm the correlation of the assessor with the best-performing patient; however, since a plurality of symptom indices are considered in the efficacy evaluation using the extended set pair analysis, and the weight of each symptom index is different; if the symptom index weights are taken into account in the calculation of ED, the ED of the evaluated patient and the ideal patient is:
wherein d (μ) l ，u * ) ED, μ, representing the degree of connection between patient/and ideal patient kl Represents the degree of contact of patient/for symptom k; if the ED is smaller, the curative effect of the patient is better; if the ED is larger, the curative effect of the patient is worse.
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